Question

Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23'', with a margin of error of {2 inches. Assuming he used a 95% confidence interval, how should view-ers interpret this news? Comment on each of these statements.
a. During 95 of the past 100 winters, the region got between 21" and 25" of snow.
b. There 's a 95% chance the region will get between 21" and 25" of snow this winter.
c. There will be between 21" and 25" of snow on the ground for 95% of the winter days.
d. Residents can be 95% sure that the area's average snowfall is between 21" and 25".
e. Residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter.

Answer 1

Answer:

d) Good, the interval is related to the variable of interest and the population mean analyzed.

Step-by-step explanation:

1) Data given

$\bar x = 23$ represent the mean

$ME=2$ represent the margin of error

$confidence=95\%=0.05$

The confidence interval for the mean is given by the following formula:

$\bar x \pm ME = 23\pm 3=(21,25)$

Where the margin of error is given by $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"

2) Analyze the possible options

a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.

b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.

c) Wrong, the confidence interval is not related to the individual days of winter.

d) Good, the interval is related to the variable of interest and the population mean analyzed.

e) Wrong, the confidence interval is not related to specific events, is related to the population mean.